Someone can help ?

What have you tried? It looks like l'Hopital's rule might be useful.

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What have you learned? I'm not going to try something without knowing whether it will help you.
 
[MATH]f’(a) = \lim_{x\to a} \dfrac{f(x)-f(a)}{x-a}[/MATH]
[MATH]a=0 \text{ and } f(x)=e^{x\sqrt{x+k}}[/MATH]
[MATH]f’(0) = \lim_{x \to 0} \dfrac{e^{x\sqrt{x+k}} - e^0}{x-0} = 12[/MATH]
can you finish and determine the value for k ?
 
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